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math.FA2023
Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines
Karlheinz Gröchenig, Irina Shafkulovska
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a…
math.FA2023
Variable Bandwidth via Wilson bases
Beatrice Andreolli, Karlheinz Gröchenig
We introduce a new concept of variable bandwidth that is based on the truncation of Wilson expansions. For this model we derive both (nonuniform) sampling theorems, the complete re…
math.FA2023
Totally Positive Functions and Gabor Frames over Rational Lattices
Karlheinz Gröchenig
We show that for an arbitrary totally positive function and rational, the Gabor family is a frame for $…